Continuity as a computational effect
This work addresses the problem of managing hybrid systems in software engineering, offering a foundational approach for developers, but it is incremental as it extends existing monadic techniques to a new domain.
The paper tackles the challenge of integrating continuous physical processes into component-based software development by encoding continuous behavior as a computational effect using a monad. The result is a framework that enables the study of continuity's impact on composition, analogous to existing monads for partial, non-deterministic, and probabilistic components.
The original purpose of component-based development was to provide techniques to master complex software, through composition, reuse and parametrisation. However, such systems are rapidly moving towards a level in which software becomes prevalently intertwined with (continuous) physical processes. A possible way to accommodate the latter in component calculi relies on a suitable encoding of continuous behaviour as (yet another) computational effect. This paper introduces such an encoding through a monad which, in the compositional development of hybrid systems, may play a role similar to the one played by the 1+, powerset, and distribution monads in the characterisation of partial, non deterministic and probabilistic components, respectively. This monad and its Kleisli category provide a setting in which the effects of continuity over (different forms of) composition can be suitably studied.